I have written more than enough about this ... enough to bore the pants off everyone, really.
But, yes, I am more or less in your size range flaccid and have the big balls also. I wear a jock, made for me by a small company in Nottingham (England).
I could wear a standard jock, just about, for a limited time for sport etc. But for any length of time the compression is uncomfortable, and an erection would be dangerous. So the ones I wear all day have custom made pouches (in fact they are totally custom made as the rear straps have to be lengthened considerably).
I could give more details if you need similar.